Going beyond “The Math Wars”: A Special Educator’s Guide to Understanding and Assisting with Inquiry-Based Teaching in Mathematics
Fundamental Questions (1): What is inquiry-based teaching in mathematics?
Inquiry-based teaching is a “student-centred approach” (Cole, J. E., & Wasburn-Moses, L. H, 2010, p. 15) that enables students to be more active and involved in their own learning processes. The main idea of inquiry-based teaching is to enable students to grasp a more conceptual understanding of mathematical content rather than memorizing the specific ways to solve mathematical equations, ultimately encouraging students to understand “why” and “how” things work.
Part-Whole Questions (1): Why do students struggle in mathematics?
One of the reasons why students struggle in mathematics is due to the lack of support and resources they receive. Many educators, and other learning supports, continuously “report a lack of materials, a lack of support, and a lack of confidence” (Cole, J. E., et al, 2010, p. 14) when teaching mathematical content, resulting in content being delivered in less engaging, less meaningful and unclear ways. Furthermore, it has been reported that “more than half of the special education teachers were unfamiliar with the standards” (Cole, J. E., et al, 2010, p. 14) of the National Council of Teachers of Mathematics (NCTM). Many students struggle in mathematics due to experiencing math anxiety and/ or lacking a necessary foundation of knowledge and skills. Further, it has been reported that disabilities in mathematics affect “5% to 8% of all K–12 students” (Cole, J. E., et al, 2010, p. 14), ultimately impacting their ability to grasp a comprehensive and conceptual understanding of what they are learning. Students with disabilities in mathematics often experience difficulty with “basic facts” and completing tasks such as “generalization, applying metacognitive strategies, discriminating key points from irrelevant information, and solving multistep problems” (Cole, J. E., et al, 2010, p. 15) effectively. The longer a student struggles in mathematics with no support will result in students needing more intensive support in the future, ultimately negatively impacting student success.
Part-Whole Questions (2): How can educators, and other learning supports, promote the learning of all students?
One of the most important steps to supporting all student learning is to collaborate with other learning support professionals to discuss instruction, interventions, adaptations, learning opportunities and more. Without a doubt, “collaboration is essential” (Cole, J. E., et al, 2010, p. 19) for student success. Educators, learning supports, families and other individuals involved in the student’s learning must have ongoing meetings to determine what is/ is not working, plans, students’ strengths and areas needing more support. Furthermore, “planning is key” (Cole, J. E., et al, 2010, p. 19) to develop and deliver meaningful and engaging content and learning experiences for students. Planning will ensure educators feel more confident teaching mathematics and enable educators to better support each student in their classroom.
Hypothesis Questions (1): If educators combine inquiry-based teaching approaches with direct instruction approaches, what would the benefits be on student learning outcomes?
Educators can make content and learning opportunities more engaging and meaningful for students by combining an inquiry-based teaching approach with a direct-instruction approach. To promote the learning of all students “the two teaching approaches can and should be combined” (Cole, J. E., et al, 2010, p. 16) within mathematical content. The combination of these two approaches is “essential to student growth in mathematics” (Cole, J. E., et al, 2010, p. 19) as it enables educators to create more meaningful and engaging learning experiences that better meet the student’s needs. Furthermore, if content and learning experiences are presented in clear and engaging ways, then students will show a decrease in having a “lack of persistence, low self-confidence, and negative attitudes toward problem-solving” (Cole, J. E., et al, 2010, p. 15) in mathematics. Lastly, when implementing these two approaches, educators must collaborate with other learning supports, resulting in all individuals being on the same page. Keeping all learning supports on the same page will create consistency for each student and ultimately promote more meaningful learning experiences.
Critical Questions (1): What are effective evidence-based strategies to teach mathematics?
- Schema-Based Instruction
Schema-based instruction in mathematics is an instructional approach that enables students to better “understand the structure of the problems they are given” (Cole, J. E., et al, 2010, p. 16), which builds off the students’ prior understanding and foundation of learning. Students can “break the problem down and diagram specific parts in order” (Cole, J. E., et al, 2010, p. 16) or backward chaining to aid them when solving mathematical problems. Educators can implement schema-based instruction alongside inquiry-based learning opportunities to encourage students to “develop their own schemas to solve various problems” (Cole, J. E., et al, 2010, p. 17) in mathematics individually or collaboratively with their peers.
- Cognitive Strategies
Cognitive strategies enable students to focus more on the “necessary steps for solving word problems successfully” (Cole, J. E., et al, 2010, p. 17) in mathematics. Three examples of cognitive strategies that students can use in mathematics are the Say, Ask, Check strategy, the STAR strategy and a checklist. The Say, Ask, Check strategy will “ensure that [students] are thinking through the problem and checking their work” (Cole, J. E., et al, 2010, p. 17) as they work on each mathematical problem. I found the description of this strategy to be vague in the reading, so I found this article that elaborates on it (https://www.interventioncentral.org/sites/default/files/pdfs/pdfs_interventions/math_meta_cog_strategy_montague_SAY_ASK_CHECK.pdf). The STAR strategy refers to steps the students can take such as “[Searching] the word problem, [Translating] the word problem, [Answering] the problem, and [Reviewing] the solution” (Cole, J. E., et al, 2010, p. 17) as they work through various mathematical problems. Checklists can be beneficial for students to “stay on task, both academically and behaviorally” (Cole, J. E., et al, 2010, p. 17), and to follow the various steps to solve equations, while checking off the tasks as they complete them.
- Scaffolding
Scaffolding is a strategy of “building new instruction onto previously taught skills” (Cole, J. E., et al, 2010, p. 17) to encourage students to apply what they already know to new skills and knowledge. Further, scaffolding promotes educators to elaborate on why learning a particular skill or content is important and how it will be applied in their future lives. Educators can scaffold through “modelling, guided practice, independent practice, and immediate corrective feedback” (Cole, J. E., et al, 2010, p. 17) as they present needed skills and content to students.
- Peer-Mediated Instruction
Peer-mediated instruction is a strategy where students work in pairs on “structured, individualized activities” (Cole, J. E., et al, 2010, p. 17) to obtain a more conceptual understanding. This strategy will enable students to “[move] from a mastered problem type to a slightly more complex problem” (Cole, J. E., et al, 2010, p. 15) with the guidance of a peer. Peer-mediated instruction must be pre-planned before being utilized to ensure all students are successful. Educators must first determine what “higher performing students are paired with lower performing students” (Cole, J. E., et al, 2010, p. 17) to benefit both students’ learning. Educators must also demonstrate the expectations of the partnered sessions to ensure students are on track and making progress with their learning.
- Concrete-Representational-Abstract (CRA) Sequence
The Concrete-Representational-Abstract (CRA) Sequence is a strategy educators can use to enable students to understand content through the “use of concrete manipulatives, representational pictures, and abstract symbols” (Cole, J. E., et al, 2010, p. 18) in mathematics. This strategy permits content and student learning to become more accessible for all students. It is recommended that the concrete-representational-abstract (CRA) sequence strategy is used “for students at all levels of math instruction” (Cole, J. E., et al, 2010, p. 18) and started early in the primary grades to promote a better conceptual understanding.
- Mnemonics
The mnemonic strategy promotes more “memorization rather than conceptual understanding” (Cole, J. E., et al, 2010, p. 19) for the students regarding content and materials. Some ways to use this strategy are through rhymes, visual representations and acronyms to remember mathematical content, formulas and procedures. ROYGBIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet) or BEDMAS (Brackets, Exponents, Division/Multiplication, Addition/Subtraction) are good representations of common examples of mnemonic strategies we often use. The mnemonic strategy “can be either teacher-or student-created” (Cole, J. E., et al, 2010, p. 19), therefore it can be easily applied within the classroom. Though this strategy does not help students gain a conceptual understanding, it does help students to remember content, formulas and procedures.
Critical Questions (2): What is my opinion on this article?
I believe combining both strategies are an important task that educators should do throughout the school year. Not every strategy or method works for every student, therefore implementing different ways to engage the learners will promote the learning of all students in the classroom. For educators, trial and error occur every day. One day something might work, then the next day it might not. We adapt to our students’ needs as they change – most needs do not stay the same forever. Lastly, educators must collaborate with their team and other learning supports because two brains are better than one – we are there to support one another to make evidence-based strategies and to provide support for each of our students as a team.
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